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( brane induced gravity Einstein bulk Einstein Einstein Einstein fine-tuning ) bulk Einstein Schwarzshild (A) bulk (B)waped bulk (C)Einstwin-Hilbert Einstein 3+1 Einstein gravity explaines and why the Newtonian potential 1/distance. (^_^)(^_^) It is derived via the Schwarzschild solution under the anzatse static, spherical, asymptotically flat, empty except for the core Can the braneworld theory reproduce the successes and ? "Braneworld" It is not trivial because we have no Einstein eq. on the brane. The brane metric cannot be dynamical variable of the brane, becaus it cannot fully specify the state of the brane. The dynamical variable should be the brane-position variable, and brane metric is induced variable from them. In order to clarify the situations, we derive here the general solution of the braneworld dynamics under the Schwarzschid anzats. 1. Introduction: Braneworld Dynamics (, _, )? why gravity motions are universal, : our 3+1 spacetime is embedded in higher dim.

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general solution with arbitrary functions, a, c, v We further impose existence of asymptotic expansion The key eq. implies Z 0 arbitrary, etc. Expand a, c, & v as Then, for the next use general solution with arbitrary functions, a, c, v in

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We further impose existence of asymptotic expansion The key eq. implies Z 0 arbitrary, etc. Expand a, c, & v as Then, general solution with arbitrary functions, a, c, v in asymptotic expansion Z 0 arbitrary, where, etc., with a i, c i & v i by for the next use

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The system has the Randall Sundrum type solution withand For | |>, this satisfies empty bulk Einestein eq. For | |, matter exists, and F takes appropriate form according to the matter distributions. The Nambu-Goto eq. is satisfied by the collective mode. We do not specify the matter motions except for the collective mode, which is 0 in the present coordinate system. ( ** ) (*) (*) From ( * ) & ( ** ), General solution for3.

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The system has the Randall Sundrum type solution For | |>, this satisfies empty bulk Einestein eq. For | |, matter exists, and F takes appropriate form according to the matter distributions. The Nambu-Goto eq. is satisfied by the collective mode. We do not specify the matter motions except for the collective mode, which is 0 in the present coordinate system. (*) (*) From ( * ) & ( ** ), withand ( ** ) General solution for3.Randall Sundrum solution (*) (*)

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Now, we seek for the general solution which tends to ( * ) as r at least near the brane. (*) (*) Randall Sundrum solution Then, as r We assume that the brane-generating interactions are much stronger than the gravity at short distances of O( ), while their gravitations are much weaker than those by the core of the sphere. Then, in | | is independent of r, and so does as r